1. Field of the Invention
Methods and systems consistent with the present invention relate to sampling frequency offset tracking and orthogonal frequency division multiplexing (OFDM) systems applied thereto, and more particularly, to a sampling frequency offset tracking method for reducing an estimation search region when a sampling frequency offset is tracked using maximum likelihood estimation (MLE), and an OFDM system which employs the sampling frequency offset tracking method.
2. Description of the Related Art
An OFDM technique splits a broadband transmission to a plurality of narrowband parallel transmissions by converting an incoming serial data sequence to parallel data of a certain block unit and multiplexing the parallel symbols to different orthogonal carrier frequencies. The OFDM technique is robust to multipath fading in a wireless communication environment, and allows data transmission at a high rate.
In an OFDM system, a sampling frequency offset tracking mostly takes advantage of pilot subcarriers. In the scheme using the pilot subcarriers, a receiving end performs synchronization using data which is known to both of a transmitting end and the receiving end and called pilot symbols. Oscillators are employed to configure a digital-to-analog converter (DAC) or an analog-to-digital converter (ADC) which is used for the signal conversion at the OFDM transmitting end and receiving end. The oscillators of the transmitting end and the receiving end do not have exactly the same period.
Such a sampling frequency offset rotates subcarriers, and this causes the inconsistence of a sampling instance. As a result, intercarrier interference (ICI) and signal to noise ratio (SNR) loss occur and thus the orthogonality of the subcarrier is destroyed.
FIGS. 1A and 1B are diagrams for illustrating effects of a sampling frequency offset in a time domain. Specifically, FIG. 1A demonstrates a positive sampling frequency offset, and FIG. 1B demonstrates a negative sampling frequency offset.
Referring first to FIG. 1A, when a sampling time at the transmitting end is faster than a sampling time at the receiving end, the sampling time difference between the transmitting end and the receiving end increases as time goes by. After a certain time period, one sample at the receiving end is left over in comparison with the number of samples at the transmitting end, and thus 1-sample robbing is required.
Referring to FIG. 1B, when the sampling time at the transmitting end is later than the sampling time at the receiving end, the sampling time difference between the transmitting end and the receiving end increases as time goes by similarly to the case as shown in FIG. 1A. After a certain time period, the number of the samples at the receiving end is greater than the number of samples at the transmitting end, and thus 1-sample stuffing is required.
FIG. 2 is a graph for illustrating effects of a sampling frequency offset in a time domain.
Referring to FIG. 2, the subcarrier index has a linear relation with the phase difference of the sampling frequency offset in the time domain. Since the sampling frequency offset varies the timing offset for each OFDM symbol, the degree of the phase rotation differs in the frequency domain. As shown in FIG. 2, as the OFDM symbol index increases, the amount of the phase change also increases.
Accordingly, it is necessary to compensate the difference of the number of samples due to the frequency offset by accurately tracking the sampling frequency offset, compensating the phase change due to the frequency offset in the frequency domain, and robbing or stuffing a sample in the time domain.
Amongst conventional sampling frequency offset tracking methods, a maximum likelihood estimation (MLE) method tracks the sampling frequency offset by calculating correlations between pilot signals which are predefined according to a resolution, and received pilot signals and detecting a pilot signal having a maximum correlation. At this time, the MLE can be expressed as below.
[Equation 1]
      Δ    ⁢                  ⁢                  t        ^            m        =            max      t        ⁢          {                                                            ∑                              k                =                0                                                              N                  p                                -                1                                      ⁢                                                  ⁢                                                            Y                                      m                    ,                    k                                                  ⁡                                  [                                                            X                      k                                        ⁢                                          ⅇ                                              j                        ⁢                                                                                                  ⁢                        2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                  kt                          /                          n                                                                                                      ]                                            *                                                2            }      
In Equation 1, Δt is a sampling frequency offset, Ym,k is a k-th pilot subcarrier of a m-th OFDM symbol, and Xk is a k-th reference pilot subcarrier. t denotes a sampling timing offset, and M denotes a resolution of the sampling timing offset. tε[−1, −1/M, . . . , 0, . . . , 1/M, . . . , 1], and t is (2M+1) in total.
Performance and complexity of the sampling frequency offset track using the MLE depend on a sampling resolution M which indicates the sampling timing offset. For instance, if a resolution is 16, it is possible to split up to time errors corresponding to 1/16=0.0625 of the sampling time.
However, according to the conventional MLE, in case that the number of symbols N is 128, the number of pilot subcarriers Np is 12, and the resolution of the sampling timing offset M is 16, the number of complex multiplications is (2M+1)NP=396 in accordance with Equation 1. Thus, the sampling frequency offset tracking becomes complicated.
According to ultra wide band (UWB) multiband OFDM Alliance (MBOA), one OFDM symbol consists of 165 samples with respect to a sampling frequency at 528 MHz. In this situation, when a single complex multiplier is employed, 396/165=2.4 OFDM symbol time is required. Thus, when the offset tracking is required for every OFDM symbol, the tracking method using only one complex multiplier is not applicable. In case that three complex multipliers are utilized in parallel, 0.77 OFDM symbol time is required and thus the estimation is feasible for every OFDM symbol. However, when a plurality of complex multipliers is used, the complexity and the power consumption of the OFDM receiver drastically increase.